1 #include "FEATURE/uwin" 2 3 #if !_UWIN 4 5 void _STUB_log(){} 6 7 #else 8 9 /* 10 * Copyright (c) 1992, 1993 11 * The Regents of the University of California. All rights reserved. 12 * 13 * Redistribution and use in source and binary forms, with or without 14 * modification, are permitted provided that the following conditions 15 * are met: 16 * 1. Redistributions of source code must retain the above copyright 17 * notice, this list of conditions and the following disclaimer. 18 * 2. Redistributions in binary form must reproduce the above copyright 19 * notice, this list of conditions and the following disclaimer in the 20 * documentation and/or other materials provided with the distribution. 21 * 3. Neither the name of the University nor the names of its contributors 22 * may be used to endorse or promote products derived from this software 23 * without specific prior written permission. 24 * 25 * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND 26 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 27 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 28 * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE 29 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 30 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 31 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 32 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 33 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 34 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 35 * SUCH DAMAGE. 36 */ 37 38 #ifndef lint 39 static char sccsid[] = "@(#)log.c 8.2 (Berkeley) 11/30/93"; 40 #endif /* not lint */ 41 42 #include <math.h> 43 #include <errno.h> 44 45 #include "mathimpl.h" 46 47 /* Table-driven natural logarithm. 48 * 49 * This code was derived, with minor modifications, from: 50 * Peter Tang, "Table-Driven Implementation of the 51 * Logarithm in IEEE Floating-Point arithmetic." ACM Trans. 52 * Math Software, vol 16. no 4, pp 378-400, Dec 1990). 53 * 54 * Calculates log(2^m*F*(1+f/F)), |f/j| <= 1/256, 55 * where F = j/128 for j an integer in [0, 128]. 56 * 57 * log(2^m) = log2_hi*m + log2_tail*m 58 * since m is an integer, the dominant term is exact. 59 * m has at most 10 digits (for subnormal numbers), 60 * and log2_hi has 11 trailing zero bits. 61 * 62 * log(F) = logF_hi[j] + logF_lo[j] is in tabular form in log_table.h 63 * logF_hi[] + 512 is exact. 64 * 65 * log(1+f/F) = 2*f/(2*F + f) + 1/12 * (2*f/(2*F + f))**3 + ... 66 * the leading term is calculated to extra precision in two 67 * parts, the larger of which adds exactly to the dominant 68 * m and F terms. 69 * There are two cases: 70 * 1. when m, j are non-zero (m | j), use absolute 71 * precision for the leading term. 72 * 2. when m = j = 0, |1-x| < 1/256, and log(x) ~= (x-1). 73 * In this case, use a relative precision of 24 bits. 74 * (This is done differently in the original paper) 75 * 76 * Special cases: 77 * 0 return signalling -Inf 78 * neg return signalling NaN 79 * +Inf return +Inf 80 */ 81 82 #if defined(vax) || defined(tahoe) 83 #define _IEEE 0 84 #define TRUNC(x) x = (double) (float) (x) 85 #else 86 #define _IEEE 1 87 #define endian (((*(int *) &one)) ? 1 : 0) 88 #define TRUNC(x) *(((int *) &x) + endian) &= 0xf8000000 89 #define infnan(x) 0.0 90 #endif 91 92 #define N 128 93 94 /* Table of log(Fj) = logF_head[j] + logF_tail[j], for Fj = 1+j/128. 95 * Used for generation of extend precision logarithms. 96 * The constant 35184372088832 is 2^45, so the divide is exact. 97 * It ensures correct reading of logF_head, even for inaccurate 98 * decimal-to-binary conversion routines. (Everybody gets the 99 * right answer for integers less than 2^53.) 100 * Values for log(F) were generated using error < 10^-57 absolute 101 * with the bc -l package. 102 */ 103 static double A1 = .08333333333333178827; 104 static double A2 = .01250000000377174923; 105 static double A3 = .002232139987919447809; 106 static double A4 = .0004348877777076145742; 107 108 static double logF_head[N+1] = { 109 0., 110 .007782140442060381246, 111 .015504186535963526694, 112 .023167059281547608406, 113 .030771658666765233647, 114 .038318864302141264488, 115 .045809536031242714670, 116 .053244514518837604555, 117 .060624621816486978786, 118 .067950661908525944454, 119 .075223421237524235039, 120 .082443669210988446138, 121 .089612158689760690322, 122 .096729626458454731618, 123 .103796793681567578460, 124 .110814366340264314203, 125 .117783035656430001836, 126 .124703478501032805070, 127 .131576357788617315236, 128 .138402322859292326029, 129 .145182009844575077295, 130 .151916042025732167530, 131 .158605030176659056451, 132 .165249572895390883786, 133 .171850256926518341060, 134 .178407657472689606947, 135 .184922338493834104156, 136 .191394852999565046047, 137 .197825743329758552135, 138 .204215541428766300668, 139 .210564769107350002741, 140 .216873938300523150246, 141 .223143551314024080056, 142 .229374101064877322642, 143 .235566071312860003672, 144 .241719936886966024758, 145 .247836163904594286577, 146 .253915209980732470285, 147 .259957524436686071567, 148 .265963548496984003577, 149 .271933715484010463114, 150 .277868451003087102435, 151 .283768173130738432519, 152 .289633292582948342896, 153 .295464212893421063199, 154 .301261330578199704177, 155 .307025035294827830512, 156 .312755710004239517729, 157 .318453731118097493890, 158 .324119468654316733591, 159 .329753286372579168528, 160 .335355541920762334484, 161 .340926586970454081892, 162 .346466767346100823488, 163 .351976423156884266063, 164 .357455888922231679316, 165 .362905493689140712376, 166 .368325561158599157352, 167 .373716409793814818840, 168 .379078352934811846353, 169 .384411698910298582632, 170 .389716751140440464951, 171 .394993808240542421117, 172 .400243164127459749579, 173 .405465108107819105498, 174 .410659924985338875558, 175 .415827895143593195825, 176 .420969294644237379543, 177 .426084395310681429691, 178 .431173464818130014464, 179 .436236766774527495726, 180 .441274560805140936281, 181 .446287102628048160113, 182 .451274644139630254358, 183 .456237433481874177232, 184 .461175715122408291790, 185 .466089729924533457960, 186 .470979715219073113985, 187 .475845904869856894947, 188 .480688529345570714212, 189 .485507815781602403149, 190 .490303988045525329653, 191 .495077266798034543171, 192 .499827869556611403822, 193 .504556010751912253908, 194 .509261901790523552335, 195 .513945751101346104405, 196 .518607764208354637958, 197 .523248143765158602036, 198 .527867089620485785417, 199 .532464798869114019908, 200 .537041465897345915436, 201 .541597282432121573947, 202 .546132437597407260909, 203 .550647117952394182793, 204 .555141507540611200965, 205 .559615787935399566777, 206 .564070138285387656651, 207 .568504735352689749561, 208 .572919753562018740922, 209 .577315365035246941260, 210 .581691739635061821900, 211 .586049045003164792433, 212 .590387446602107957005, 213 .594707107746216934174, 214 .599008189645246602594, 215 .603290851438941899687, 216 .607555250224322662688, 217 .611801541106615331955, 218 .616029877215623855590, 219 .620240409751204424537, 220 .624433288012369303032, 221 .628608659422752680256, 222 .632766669570628437213, 223 .636907462236194987781, 224 .641031179420679109171, 225 .645137961373620782978, 226 .649227946625615004450, 227 .653301272011958644725, 228 .657358072709030238911, 229 .661398482245203922502, 230 .665422632544505177065, 231 .669430653942981734871, 232 .673422675212350441142, 233 .677398823590920073911, 234 .681359224807238206267, 235 .685304003098281100392, 236 .689233281238557538017, 237 .693147180560117703862 238 }; 239 240 static double logF_tail[N+1] = { 241 0., 242 -.00000000000000543229938420049, 243 .00000000000000172745674997061, 244 -.00000000000001323017818229233, 245 -.00000000000001154527628289872, 246 -.00000000000000466529469958300, 247 .00000000000005148849572685810, 248 -.00000000000002532168943117445, 249 -.00000000000005213620639136504, 250 -.00000000000001819506003016881, 251 .00000000000006329065958724544, 252 .00000000000008614512936087814, 253 -.00000000000007355770219435028, 254 .00000000000009638067658552277, 255 .00000000000007598636597194141, 256 .00000000000002579999128306990, 257 -.00000000000004654729747598444, 258 -.00000000000007556920687451336, 259 .00000000000010195735223708472, 260 -.00000000000017319034406422306, 261 -.00000000000007718001336828098, 262 .00000000000010980754099855238, 263 -.00000000000002047235780046195, 264 -.00000000000008372091099235912, 265 .00000000000014088127937111135, 266 .00000000000012869017157588257, 267 .00000000000017788850778198106, 268 .00000000000006440856150696891, 269 .00000000000016132822667240822, 270 -.00000000000007540916511956188, 271 -.00000000000000036507188831790, 272 .00000000000009120937249914984, 273 .00000000000018567570959796010, 274 -.00000000000003149265065191483, 275 -.00000000000009309459495196889, 276 .00000000000017914338601329117, 277 -.00000000000001302979717330866, 278 .00000000000023097385217586939, 279 .00000000000023999540484211737, 280 .00000000000015393776174455408, 281 -.00000000000036870428315837678, 282 .00000000000036920375082080089, 283 -.00000000000009383417223663699, 284 .00000000000009433398189512690, 285 .00000000000041481318704258568, 286 -.00000000000003792316480209314, 287 .00000000000008403156304792424, 288 -.00000000000034262934348285429, 289 .00000000000043712191957429145, 290 -.00000000000010475750058776541, 291 -.00000000000011118671389559323, 292 .00000000000037549577257259853, 293 .00000000000013912841212197565, 294 .00000000000010775743037572640, 295 .00000000000029391859187648000, 296 -.00000000000042790509060060774, 297 .00000000000022774076114039555, 298 .00000000000010849569622967912, 299 -.00000000000023073801945705758, 300 .00000000000015761203773969435, 301 .00000000000003345710269544082, 302 -.00000000000041525158063436123, 303 .00000000000032655698896907146, 304 -.00000000000044704265010452446, 305 .00000000000034527647952039772, 306 -.00000000000007048962392109746, 307 .00000000000011776978751369214, 308 -.00000000000010774341461609578, 309 .00000000000021863343293215910, 310 .00000000000024132639491333131, 311 .00000000000039057462209830700, 312 -.00000000000026570679203560751, 313 .00000000000037135141919592021, 314 -.00000000000017166921336082431, 315 -.00000000000028658285157914353, 316 -.00000000000023812542263446809, 317 .00000000000006576659768580062, 318 -.00000000000028210143846181267, 319 .00000000000010701931762114254, 320 .00000000000018119346366441110, 321 .00000000000009840465278232627, 322 -.00000000000033149150282752542, 323 -.00000000000018302857356041668, 324 -.00000000000016207400156744949, 325 .00000000000048303314949553201, 326 -.00000000000071560553172382115, 327 .00000000000088821239518571855, 328 -.00000000000030900580513238244, 329 -.00000000000061076551972851496, 330 .00000000000035659969663347830, 331 .00000000000035782396591276383, 332 -.00000000000046226087001544578, 333 .00000000000062279762917225156, 334 .00000000000072838947272065741, 335 .00000000000026809646615211673, 336 -.00000000000010960825046059278, 337 .00000000000002311949383800537, 338 -.00000000000058469058005299247, 339 -.00000000000002103748251144494, 340 -.00000000000023323182945587408, 341 -.00000000000042333694288141916, 342 -.00000000000043933937969737844, 343 .00000000000041341647073835565, 344 .00000000000006841763641591466, 345 .00000000000047585534004430641, 346 .00000000000083679678674757695, 347 -.00000000000085763734646658640, 348 .00000000000021913281229340092, 349 -.00000000000062242842536431148, 350 -.00000000000010983594325438430, 351 .00000000000065310431377633651, 352 -.00000000000047580199021710769, 353 -.00000000000037854251265457040, 354 .00000000000040939233218678664, 355 .00000000000087424383914858291, 356 .00000000000025218188456842882, 357 -.00000000000003608131360422557, 358 -.00000000000050518555924280902, 359 .00000000000078699403323355317, 360 -.00000000000067020876961949060, 361 .00000000000016108575753932458, 362 .00000000000058527188436251509, 363 -.00000000000035246757297904791, 364 -.00000000000018372084495629058, 365 .00000000000088606689813494916, 366 .00000000000066486268071468700, 367 .00000000000063831615170646519, 368 .00000000000025144230728376072, 369 -.00000000000017239444525614834 370 }; 371 372 #if !_lib_log 373 374 extern double 375 #ifdef _ANSI_SOURCE 376 log(double x) 377 #else 378 log(x) double x; 379 #endif 380 { 381 int m, j; 382 double F, f, g, q, u, u2, v, zero = 0.0, one = 1.0; 383 volatile double u1; 384 385 /* Catch special cases */ 386 if (x <= 0) 387 if (_IEEE && x == zero) /* log(0) = -Inf */ 388 return (-one/zero); 389 else if (_IEEE) /* log(neg) = NaN */ 390 return (zero/zero); 391 else if (x == zero) /* NOT REACHED IF _IEEE */ 392 return (infnan(-ERANGE)); 393 else 394 return (infnan(EDOM)); 395 else if (!finite(x)) 396 if (_IEEE) /* x = NaN, Inf */ 397 return (x+x); 398 else 399 return (infnan(ERANGE)); 400 401 /* Argument reduction: 1 <= g < 2; x/2^m = g; */ 402 /* y = F*(1 + f/F) for |f| <= 2^-8 */ 403 404 m = logb(x); 405 g = ldexp(x, -m); 406 if (_IEEE && m == -1022) { 407 j = logb(g), m += j; 408 g = ldexp(g, -j); 409 } 410 j = N*(g-1) + .5; 411 F = (1.0/N) * j + 1; /* F*128 is an integer in [128, 512] */ 412 f = g - F; 413 414 /* Approximate expansion for log(1+f/F) ~= u + q */ 415 g = 1/(2*F+f); 416 u = 2*f*g; 417 v = u*u; 418 q = u*v*(A1 + v*(A2 + v*(A3 + v*A4))); 419 420 /* case 1: u1 = u rounded to 2^-43 absolute. Since u < 2^-8, 421 * u1 has at most 35 bits, and F*u1 is exact, as F has < 8 bits. 422 * It also adds exactly to |m*log2_hi + log_F_head[j] | < 750 423 */ 424 if (m | j) 425 u1 = u + 513, u1 -= 513; 426 427 /* case 2: |1-x| < 1/256. The m- and j- dependent terms are zero; 428 * u1 = u to 24 bits. 429 */ 430 else 431 u1 = u, TRUNC(u1); 432 u2 = (2.0*(f - F*u1) - u1*f) * g; 433 /* u1 + u2 = 2f/(2F+f) to extra precision. */ 434 435 /* log(x) = log(2^m*F*(1+f/F)) = */ 436 /* (m*log2_hi+logF_head[j]+u1) + (m*log2_lo+logF_tail[j]+q); */ 437 /* (exact) + (tiny) */ 438 439 u1 += m*logF_head[N] + logF_head[j]; /* exact */ 440 u2 = (u2 + logF_tail[j]) + q; /* tiny */ 441 u2 += logF_tail[N]*m; 442 return (u1 + u2); 443 } 444 445 #endif 446 447 /* 448 * Extra precision variant, returning struct {double a, b;}; 449 * log(x) = a+b to 63 bits, with a is rounded to 26 bits. 450 */ 451 struct Double 452 #ifdef _ANSI_SOURCE 453 __log__D(double x) 454 #else 455 __log__D(x) double x; 456 #endif 457 { 458 int m, j; 459 double F, f, g, q, u, v, u2, one = 1.0; 460 volatile double u1; 461 struct Double r; 462 463 /* Argument reduction: 1 <= g < 2; x/2^m = g; */ 464 /* y = F*(1 + f/F) for |f| <= 2^-8 */ 465 466 m = (int)logb(x); 467 g = ldexp(x, -m); 468 if (_IEEE && m == -1022) { 469 j = (int)logb(g), m += j; 470 g = ldexp(g, -j); 471 } 472 j = (int)(N*(g-1) + .5); 473 F = (1.0/N) * j + 1; 474 f = g - F; 475 476 g = 1/(2*F+f); 477 u = 2*f*g; 478 v = u*u; 479 q = u*v*(A1 + v*(A2 + v*(A3 + v*A4))); 480 if (m | j) 481 u1 = u + 513, u1 -= 513; 482 else 483 u1 = u, TRUNC(u1); 484 u2 = (2.0*(f - F*u1) - u1*f) * g; 485 486 u1 += m*logF_head[N] + logF_head[j]; 487 488 u2 += logF_tail[j]; u2 += q; 489 u2 += logF_tail[N]*m; 490 r.a = u1 + u2; /* Only difference is here */ 491 TRUNC(r.a); 492 r.b = (u1 - r.a) + u2; 493 return (r); 494 } 495 496 #endif 497